Unit 5

Systems of Linear Equations

In Unit 5, you will learn about the fundamentals of systems of equations and how they can be used to solve real-world problems. We will cover topics such as solving systems graphically, algebraically, and using substitution or elimination methods. You will also have the opportunity to work on various practical exercises and engage in group discussions to strengthen your understanding.

When we say we want to find the solution to a system of equations, we are trying to find where they cross. It is important to remember that every equation represents a line. In this unit, we are only dealing with linear equations which are straight lines. If we have a system of equations, we have multiple lines. The solution to that system is the coordinates of where those lines cross.

After we investigate systems of equations, we will use the tools we have learned to also interpret and write systems of inequalities. We solve the relatively the same way, but it is important to remember that inequalities can have more than one answer. If we are given x < 7, then we can pick any number that is less than 7 and they are all correct answers. We will explore how this affects our solutions.

Lesson 1

In Lesson 1, we cover a lot of material. We learn how to find the solution to a system of equations using algebra, graphs, and tables. Throughout this unit we will mostly focus on using algebra, but it is important to know each method.

Solving Systems of Equations By Graphing

Solving Systens by Graphing - MathHelp.com - Algebra Help

I can solve systems of linear equations using tables

Solve a system of linear equations using substitution

Solving linear systems by substitution | Algebra Basics | Khan Academy

Lesson 2

In lesson 2 we take our first look at 2-variable inequalities and equations. We are first going to look at what we call linear constraints (restrictions) and how they can be written as inequalities.

Writing two-variable inequalities word problem | Mathematics I | High School Math | Khan Academy

Write an inequality from a word problem

Lesson 3 and 4

In these lessons we are going to learn about graphing equations that have more than one variable, and then investigating how that graph would change if we make it an inequality.

There are 3 different forms of equations that we will need to know how to use and graph: slope-intercept form, point-slope form, and standard form.

In Lesson 3 we will talk about graphing inequalities in 2 variables, which is done in a similar way to graphing equations but with slight differences. I have added these videos at the end of this section.

How to Graph Lines in Slope Intercept Form (y=mx+b)

Graphing a linear equation by rewriting from standard form to slope intercept form

How To Graph Linear Equations In Point Slope Form | Algebra

Graph a Line in Point Slope Form

Graphing Lines in Standard Form

Graphing Linear Equations in Standard Form by Finding Intercepts

Graphing Systems of Inequalities

Graphing Linear Inequalities || Solution Set, Solid/Dotted Line, Shading | Algebra 1

Lesson 5 - 7

In these lessons, we are practicing what we have already learned. I have attached some videos that go deeper in graphing constraints when given to us as story problems, along with some videos about interpreting graphs to find possible solutions.

Represent constraints in story problems using inequalities

Represent Constraints Symbolically and Graphically

Determine if the Point is a Solution to the System of Equations Easy Example

How to determine if a point is a solution to a System of Linear Inequalities

Lesson 8 and 9

In these lessons, we are going to learn about a new method to solving a system of equations called Elimination. This method is exactly how it sounds. To solve for one of the variables, we must eliminate the other. It is important to be able to identify when elimination is going to be easier or more difficult than substitution. Here are some videos explaining this method, and explaining when to use it.

Solving Systems of Equations with Elimination (Multiplying First)

Solving Systems of Equations... Elimination Method (NancyPi)

Algebra 37- Solving Systems of Equations by Elimination

How to tell if you use substitution or elimination when solving systems of equations

Lesson 10

In our final lesson of Unit 5, we are going to look into different types of solutions in systems of equations. Is it possible for systems of equations to have no solutions? How about an infinite number of solutions? Oh you betcha, eh. Here's some explanations and examples of how to find out which case you are dealing with.

Types of Solutions - Infinite, No solution, Unique Solution EXAMPLES

Algebra Equations (No Solution, One Solution, and Infinite Solutions)

Extra Practice

You did it! But maybe not as well as you would have liked? That's okay. Here are some practice problems.

Systems of equations | Algebra 1 | Math | Khan AcademyIf one line is useful, let's see what we can do with two lines. In this unit, we learn how to write systems of equations, solve those systems, and interpret what those solutions mean in a real-world context.

Inequalities (systems & graphs) | Algebra 1 | Math | Khan AcademyIf it takes someone in a cooking competition 30 seconds to chop an onion and 18 seconds to chop a carrot, and their goal is to chop at least 20 of these vegetables in a time limit of 540 seconds, what can they do? Use a system of linear inequalities, of course.

Unit 5 Assessment Review Video

Alg U5 Review (1).mp4

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